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Reference for Y. Manin's idea of "algebraic geometry over the symmetric monoidal model category of motives."

Has been sugested to me that this was made in a Manin's letter. There is an escaned copy?

Some work in this direction has been made in the thesis of Spitzweck, but I refer to first references of Manin.

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    $\begingroup$ Why not ask Manin himself for a copy? $\endgroup$
    – Dmitri Pavlov
    Commented Apr 12, 2016 at 11:09
  • $\begingroup$ @Dmitri Ok, but I would be interested in an (online) copy for the community. Thanks! $\endgroup$
    – tttbase
    Commented Apr 22, 2016 at 1:27
  • $\begingroup$ Again, you could ask Manin if you can put it online. He probably doesn't mind… $\endgroup$
    – Dmitri Pavlov
    Commented Apr 22, 2016 at 6:45

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The only reference ever given for this is

Y. Manin, Letter, March 2000

I don't think this letter (from Manin to Bertrand Toen, I presume) has ever been made public, and definitely it hasn't been published. But you might want to try asking Toen for a copy.

As you known, some of the math involved was worked out in Spitzweck's thesis, "Operads, Algebras and Modules in Model Categories and Motives". Note that he thanks Toen in the introduction, and Manin is listed as "Korreferent".

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Not really an answer, but as a complement to Myshkin's, let me just mention a predecessor : Deligne's very famous (and magnificent) article

Deligne, P. Le groupe fondamental de la droite projective moins trois points.

available here

especially the two paragraphs

§5 Géométrie algébrique dans une catégorie tannakienne

§7 Géométrie algébrique dans la catégorie tannakienne des systèmes de réalisations: interprétations

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  • $\begingroup$ Also "Catégories Tannakiennes, P. deligne The Festschrift II". $\endgroup$
    – tttbase
    Commented Apr 15, 2016 at 1:36

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